Answer
$x=-3$, $y=-2$, see graph
Work Step by Step
Consider the linear equation
$2x+3y+6=0$
Use intercepts to graph the given equation as follows:
Step 1: Find the $x$ intercept.
To get the x intercept of line, substitute $y=0$ in the line and find the value of x.
$\begin{align}
& 2x+3\times 0+6=0 \\
& 2x=-6 \\
& x=\frac{\left( -6 \right)}{2} \\
& =-3
\end{align}$
So, the $x$ intercept of the equation $2x+3y+6=0$ is $-3$. Hence, the line passes through $\left( -3,0 \right)$.
Step 2: Find the $y$ intercept.
To calculate the y intercept, substitute $x=0$ in the given equation and find the value of y:
$\begin{align}
& 2\times 0+3y+6=0 \\
& 3y=-6 \\
& y=\frac{\left( -6 \right)}{3} \\
& =-2
\end{align}$
So, the $y$ intercept of the given equation $2x+3y+6=0$ is $-2$. Hence, the line passes through $\left( 0,-2 \right)$.
Step 3: Graph the equation of the straight line.
Locate two points containing intercepts $\left( -3,0 \right)$ and $\left( 0,-2 \right)$. Connect them by a straight line.
The graph of the given equation $2x+3y+6=0$ is as follows:
